A Hybrid Update of the Fe-Si System by DSC, Thermodynamic Modeling and Statistical Learning from Ladle Refining Data of Electrical Steels

Abstract Electrical steels, also known as silicon steels, are essential materials in electrical applications due to their unique magnetic properties, which are enhanced by adding up to 3.5 wt pct Si. However, alloying with ferrosilicon FeSi75, a mixture of 25 wt pct Fe and 75 wt pct Si, during ladle refining faces steelmakers with metallurgical challenges, primarily due to the strong exothermic reaction during its dissolution in liquid steel. Here, solution thermodynamics of the Fe-Si system offer insights into the heat evolution and, therefore, superheating control for continuous casting. This study experimentally reassesses the binary Fe-Si system using Differential Scanning Calorimetry (DSC) and High-Temperature Laser Scanning Confocal Microscopy (HT-LSCM) to investigate phase equilibria between 0.50 and 12.50 wt pct Si and from 600 °C to 1550 °C. Thermodynamic modeling of the Fe-Si system was carried out in the CALPHAD framework, applying the Modified Quasichemical Model (MQM) for the liquid phase to consider the strong interactions between Fe and Si. In this way, the description of the liquid’s mixing enthalpy and the activities of Fe and Si agree well with literature values. Deviations in liquidus and solidus temperatures, as measured by DSC, were reduced to within ± 5 °C. Additionally, the solubility limits of Fe and Si in intermediate silicides were refined based on the most recently published measurements. A comprehensive statistical analysis of industrial ladle refining processes involving 172 t ladles revealed a heat increase of 4.73 °C per t of FeSi75, consistent with adiabatic thermodynamic calculations (5 °C per t FeSi75). These findings improve the precision of thermodynamic databases and provide valuable insights for optimizing heat management and process control in producing silicon steels.